Mathlib Map

Theorems · Theorem · general topology

Set.einfsep_zero

∀ {α : Type u_1} [inst : EDist α] {s : Set α}, s.einfsep = 0 ↔ ∀ C > 0, ∃ x ∈ s, ∃ y ∈ s, x ≠ y ∧ edist x y < C
Defined in
Mathlib.Topology.MetricSpace.Infsep
Cited by
1 results in Mathlib
Foundations
Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
EDist

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • ENNRealstatement and proof · cited by 9,879
  • Bot.botproof · cited by 4,720
  • iInfproof · cited by 1,690
  • EDist.ediststatement and proof · cited by 735
  • EDiststatement and proof · cited by 91
  • Set.einfsepstatement · cited by 47

Cited by1

Results whose statement or proof uses this declaration.